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WO2008151380A1 - Procédé de traitement d'images par résonance magnétique parallèle - Google Patents

Procédé de traitement d'images par résonance magnétique parallèle Download PDF

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WO2008151380A1
WO2008151380A1 PCT/AU2008/000852 AU2008000852W WO2008151380A1 WO 2008151380 A1 WO2008151380 A1 WO 2008151380A1 AU 2008000852 W AU2008000852 W AU 2008000852W WO 2008151380 A1 WO2008151380 A1 WO 2008151380A1
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pmri
reconstruction
image
model
mri
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Jingxin Zhang
Zhaolin Chen
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Monash University
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Monash University
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Priority claimed from AU2007903201A external-priority patent/AU2007903201A0/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/48—NMR imaging systems
    • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
    • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
    • G01R33/561—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences
    • G01R33/5611—Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE

Definitions

  • the present invention relates generally to magnetic resonance imaging (MRI) and, more particularly, to improved methods of image reconstruction in parallel magnetic resonance imaging (pMRI) systems.
  • Magnetic resonance imaging is a non-invasive method which can be used to acquire and record images of the inside of a subject, which finds application in medical imaging where it is commonly used to identify pathological or other physiological alterations in living tissues, for example of a human subject.
  • MRI Magnetic resonance imaging
  • Static magnetic fields typically in the range of 0.5 to 2.0 Tesla may be generated using permanent magnets or resistive electromagnets, however in modern MRI apparatus the static fields are most commonly generated using superconducting electromagnets.
  • Typical MRI apparatus also includes three orthogonally-oriented gradient magnets.
  • the gradient magnets are conventionally resistive electromagnets which are of relatively low strength compared to the main static magnetic field.
  • the purpose of the gradient magnets is to generate a spatial variation in the magnetic field, ideally being a linear variation, which is controllable along three orthogonal axes.
  • the gradient magnets enable spatial selection of the imaging function within the subject volume.
  • NMR nuclear magnetic resonance
  • RF radio frequency
  • the nuclear spin system absorbs magnetic energy, resulting in a precession of magnetic moments of the nuclei around the direction of the main magnetic field.
  • the precessing magnetic moments undergo free induction decay (FID), releasing their absorbed energy and returning to a static state.
  • FID free induction decay
  • NMR signals are detected using one or more receiver RF coils.
  • FT imaging sequence commences by applying a slice selection gradient field, simultaneously with an RF excitation pulse.
  • the slice selective gradient results in one particular plane, or slice, within the subject volume experiencing a magnetic field whereby the nuclei within the selected plane have a Larmor frequency corresponding with the centre frequency of the RF excitation pulse. Accordingly, only the nuclei within the subject volume located within the selected slice undergo excitation under the influence of the RF pulse.
  • An orthogonal phase-encoding gradient field is then applied, along one axis of the selected slice.
  • the magnetic moment of the excited nuclei within the slice are thus caused to precess at a frequency corresponding with the local magnetic field under the influence of the phase-encoding gradient, such that the frequency of oscillation ideally varies linearly along the corresponding axis of the selected slice. Due to the variation in frequency, when the phase-encoding gradient field is removed there has been established a corresponding phase variation across the selected slice.
  • a frequency-encoding gradient field is then applied along the other, orthogonal, axis of the selected slice. This again results in a variation in frequency of precession, in the perpendicular direction across the selected slice.
  • the decaying response field is detected using the receiver RF coil, or coils.
  • the resulting acquired signal comprises the sum of the response of all excited nuclei, each of which emits a field having a phase and frequency corresponding to its particular location within the two-dimensional plane of the selected slice.
  • the additional information required may be obtained by repeating the measurement using different values of phase-encoding.
  • the applied phase shift may be changed, for example, by changing the magnitude of the phase-encoding gradient field, or by changing the length of time for which the phase-encoding gradient field is applied.
  • the end result is a plurality of acquired waveforms corresponding with the plurality of applied levels of phase-encoding.
  • each waveform is sampled and digitised in order to produce a complete data set that may be represented as a two-dimensional array, or matrix, comprising a plurality of rows and columns wherein each row corresponds with a particular acquisition and corresponding phase-encoding, and each column corresponds with a particular sample time during the acquisition of the waveform received by the receiver coil.
  • the two-dimensional array, or matrix, of phase/frequency encoded data is commonly known as a "k-space" representation of the MRI image.
  • the corresponding "image-space” matrix ie the excited spin density function which is effectively the MRI image itself, may be obtained by computing the Discrete Fourier Transform (DFT) of the k-space data. That is, k-space and image-space form a (two-dimensional) Fourier transform pair.
  • DFT Discrete Fourier Transform
  • a particular problem with MRI medical imaging is that it is necessary to make a large number of individual measurements (eg by varying the phase-encoding gradient) in order to acquire a sufficiently high-resolution image of the selected slice of the imaging subject. During the measurements, the subject, ie potentially a living human patient, must remain extremely still. It is therefore recognised as being highly desirable to accelerate the overall imaging process.
  • a "pMRI signal” comprises a plurality of signal components, one for each of a corresponding plurality of receiver coils, wherein each component may be represented as an individual matrix of digitised samples (either in k-space or image-space) as described above.
  • the pMRI signal may be under-sampled in the phase-encoding direction, as a result of which every pixel (Ze matrix element) in the image-space components represents data from multiple points in space.
  • the image arrays are accordingly “compressed”, and subject to "wrap-around” artefacts (or aliasing) in a corresponding dimension.
  • the SENSE method operates in the image domain. It requires an initial estimation by pre-imaging, and subsequent inversion of a spatial sensitivity matrix C, via the pseudo inverse C + . In many cases, this problem is ill- conditioned, particularly when significant acceleration is employed, resulting in amplification of noise and estimation errors, such that image reconstruction may be unacceptably poor.
  • the PILS technique is also an image domain method, and is a special case of SENSE. In PILS, the sensitivity functions C are assumed to be ideally localised. This avoids the need to compute a corresponding inverse matrix, but is, in practice, of limited application.
  • the assumption of ideal, localised sensitivity functions may not be valid for real MRI machines, and additionally it is not possible to take advantage of techniques, such as over-sampling, in order to improve the overall signal-to-noise ratio (SNR) of the final image.
  • SNR signal-to-noise ratio
  • the SMASH method is a k-space technique with similar limitations to the (image domain) SENSE method.
  • the AUTO SMASH method utilises specific assumptions in order to estimate the receiver coil spatial sensitivity functions C during real imaging, and accordingly generally requires a period of unaccelerated operation during initial measurements for this purpose.
  • the GRAPPA method is a generalisation of AUTO SMASH which requires similar assumptions to be made. None of the prior art techniques allow any control over the accuracy with which the receiver coil responses (ie sensitivity functions) are estimated and inverted, in relation to the extent to which additive noise and errors are propagated and amplified within the reconstructed image. It is also noteworthy that a trade-off may exist between degree of acceleration and quality of reconstructed image, but that no existing technique enables quantification or optimisation of this trade-off.
  • the present invention provides, in one aspect, a parallel magnetic resonance imaging (pMRI) reconstruction method for reconstructing an image of a subject within a magnetic resonance imaging (MRI) machine having a plurality of receiver coils, wherein accelerated imaging is performed by reducing a number of distinct MRI measurements performed while simultaneously receiving measurement data from said plurality of receiver coils, the method comprising the steps of: receiving pMRI signal data comprising digitised samples acquired from the plurality of receiver coils of the MRI machine; constructing a dynamic input-output system model of a pMRI detection process of the MRI machine, said model at least embodying a plurality of estimated spatial sensitivity functions corresponding with each of said plurality of receiver coils; determining an inverse model corresponding with said system model in accordance with an optimisation method which is adapted to minimise a measure of reconstruction error, wherein said measure of reconstruction error accounts for accuracy of image reconstruction by the inverse model in the absence of additive noise and estimation error, in combination with amplification by the inverse model of
  • the present invention advantageously enables an overall improvement in the image reconstruction by optimising over both the accuracy with which an inverse function of the spatial sensitivity of the receiver coils is established, and the corruption of the final reconstructed image due to amplification of additive noise and estimation errors.
  • improvements in the estimation of an inverse function for the MRI detection system are correlated, in pMRI image reconstruction, with the existence of ill-conditioned matrices (or functions), the inversion of which results in propagation and amplification of estimation errors and additive noise components.
  • a method that seeks to perform improved image reconstruction by more accurately estimating, and inverting, the spatial sensitivity functions of the receiver coils may actually produce inferior results due to the corresponding amplification of noise and estimation errors.
  • the present invention seeks for the first time to account for both of these contributions to overall reconstruction error, and to minimise the error resulting from the combination of both effects, using suitable optimisation techniques.
  • the spatial sensitivity functions may be embodied either via image-space representations, or via k-space representations.
  • the spatial sensitivity functions are embodied in an image-space representation as an aliasing component (AC) matrix.
  • AC aliasing component
  • the spatial sensitivity functions may be embodied in a k-space representation as a polyphase matrix.
  • the optimisation method includes minimising, according to specified criteria, a measure of performance that comprises: (a) a term corresponding with a perfect reconstruction (PR) condition; and (b) a term corresponding with a gain of the inverse model.
  • PR perfect reconstruction
  • this approach seeks to avoid producing a reconstructed image based solely upon accuracy of reconstruction, but without consideration of the effects on image quality of amplified noise and propagated errors.
  • the optimisation method includes using the HL norms of the reconstruction error system and the inverse system to measure, respectively, the deviation from PR and the gain of the inverse model, and performing an HL norm optimisation.
  • the HL norm optimisation utilises an adaptively estimated weighting factor.
  • the present invention provides a computer-implemented system for performing a parallel magnetic resonance imaging (pMRI) reconstruction method for reconstructing an image of a subject within a magnetic resonance imaging (MRI) machine having a plurality of receiver coils, wherein accelerated imaging is performed by reducing a number of distinct MRI measurements performed while simultaneously receiving measurement data from said plurality of receiver coils, the system comprising: means for receiving pMRI signal data comprising digitised samples acquired from the plurality of receiver coils of the MRI machine; means for constructing a dynamic input-output system model of a pMRI detection process of the MRI machine, said model at least embodying a plurality of estimated spatial sensitivity functions corresponding with each of said plurality of receiver coils; means for determining an inverse model corresponding with said system model in accordance with an optimisation method which is adapted to minimise a measure of reconstruction error, wherein said measure of reconstruction error accounts for accuracy of image reconstruction by the inverse model in the absence of additive noise and estimation error, in combination with amplification by the inverse
  • the means for receiving pMRI signal data, the means for constructing a system model, the means for determining an inverse model, the means for reconstructing an image, and the means for providing a reconstructed image output all comprise computer software and/or hardware components.
  • the means for receiving pMRI signal data may include a suitable input peripheral interface of a computer system, along with associated software. Suitable input interfaces include network interfaces, whereby the pMRI signal data is transferred via a data communications network, direct serial or parallel interfaces to an MRI machine, storage device interfaces for retrieving the signal data from corresponding storage media, and/or a user interface device such as a keyboard.
  • the means for providing a reconstructed image output may comprise an output peripheral interface of a computer system, such as a display, printer, or the like.
  • a reconstructed image, in digital form may be output via a network interface or a storage device interface for external storage, display and/or processing.
  • Various suitable computer arrangements, including conventional personal computer (PC) hardware, will be readily apparent to those skilled in the art.
  • the means for constructing a system model, determining an inverse model, and reconstructing an image will typically comprise software components adapted for performing suitable signal processing and/or numerical computation functions. Suitable means for implementing such software components, for any given embodiment of the invention, will be readily available to those skilled in the relevant art.
  • the present invention provides an apparatus for reconstructing an image of a subject within a magnetic resonance imaging (MRI) machine having a plurality of receiver coils, wherein accelerated imaging is performed by reducing a number of distinct MRI measurements performed while simultaneously receiving measurement data from said plurality of receiver coils, the apparatus comprising: at least one processor; at least one input peripheral interface operatively coupled to the processor; at least one output peripheral interface operatively coupled to the processor; and at least one storage medium operatively coupled to the processor, the storage medium containing program instructions for execution by the processor, said program instructions causing the processor to execute the steps of: receiving via the input peripheral interface parallel magnetic resonance imaging (pMRI) signal data comprising digitised samples acquired from the plurality of receiver coils of the MRI machine; constructing a dynamic input-output system model of a pMRI detection process of the MRI machine, said model at least embodying a plurality of estimated spatial sensitivity functions corresponding with each of said plurality of receiver coils; determining an inverse model corresponding with said system model
  • pMRI
  • Figure 1 is a block diagram representing pMRI image reconstruction as a model-matching problem in accordance with preferred embodiments of the present invention
  • FIG. 2 is a schematic diagram illustrating a processing system suitable for implementing embodiments of the invention
  • Figures 3A and 3B illustrate results of simulated pMRI image reconstruction in accordance with the prior art and with a preferred embodiment of the present invention, respectively;
  • Figures 4A, 4B, and 4C illustrate results of image reconstruction resulting from an MRI scan in accordance with the prior art and with an embodiment of the present invention.
  • Figure 5 illustrates further results of MRI image reconstruction in accordance with the prior art and with an embodiment of the present invention.
  • the pMRI image reconstruction is cast as a model-matching problem.
  • a block diagram 100 of one such embodiment, representing the reconstruction problem in image space, is depicted in Figure 1.
  • an excited spin density function P is the (two-dimensional) response function of the excited nuclei within a selected slice of a subject volume under MRI imaging.
  • the excited spin density function P (102) is detected by a plurality of receiver coils, collectively having spatial sensitivity functions represented by the blocks C (104) and ⁇ C (106).
  • the spatial sensitivity functions are not precisely known, and must be estimated. Accordingly, the system model includes an estimated part C (104) and an unknown part ⁇ C (106) which is the estimation error.
  • the detected signal is also accompanied by additive noise ⁇ (108).
  • a resulting pMRI signal S (110) incorporates the desired image function
  • the model-matching problem is thus to find the transfer function (matrix) F (112) which generates an "optimal” reconstruction P (114) of the "true” image P.
  • the model represented by the block diagram 100 includes an error signal
  • signal reconstruction may therefore be performed either in the image domain using aliasing component (AC) matrices, or in k-space using polyphase matrices.
  • AC aliasing component
  • the analysis AC matrix has the form: while the synthesis AC matrix F has the form: 0, 1,-, L-I (3)
  • an analysis polyphase matrix E may be denoted as : 0, l,---, M-I (4) while a corresponding synthesis polyphase matrix H may be denoted as: 0, ⁇ ,-, L-I (5)
  • ⁇ ( «) C(n)W ⁇ (6)
  • ⁇ diag ⁇ , W ⁇ , - , wf ⁇ ' )n ⁇
  • W is the M x M DFT matrix
  • the pseudo-inverse C + operates on both the noise ⁇ generated by estimation error ⁇ C and the random noise ⁇ . Accordingly, the SENSE method is highly sensitive to the additive noises when the condition number of C is poor, resulting in the pseudo-inverse C + having high gain. Unfortunately, this is quite likely to be the case when high acceleration is used for fast imaging.
  • preferred embodiments of the present invention provide a computerised pMRI reconstruction method for reconstructing an image of a subject within an MRI machine.
  • the MRI machine has a plurality L of receiver coils, and imaging is accelerated by a factor M, /e the number of distinct MRI measurements is reduced by this factor while simultaneously receiving measurement data from the plurality L of receiver coils. In practice, therefore, L > M.
  • the method commences by a computer receiving pMRI signal data including digitised samples acquired from the L receiver coils of the MRI machine.
  • a system model of a pMRI detection process of the MRI machine is constructed.
  • the system model embodies at least a plurality L of estimated spatial sensitivity functions corresponding with each of the L receiver coils.
  • the estimated special sensitivity functions are embodied within the analysis AC matrix C (104).
  • the estimated spatial sensitivity functions may equivalents be embodied via other means, for example, a synthesis polyphase matrix H.
  • the spatial sensitivity functions of the receiver coils of the MRI machine may be estimated using various techniques known in the art.
  • the spatial sensitivity functions of the receiver coils may be estimated by pre-imaging, such as in the prior art SENSE and PILS methods.
  • the synthesis polyphase matrix H is estimated directly during the actual imaging process, and techniques of this type may also be applicable to the present invention.
  • Embodiments of the inventive method then proceed by determining, for example via the model-matching approach previously described, an inverse model corresponding with the system model.
  • the inverse model is the transfer function (ie matrix) F (112), the purpose of which, as previously discussed, is to generate an optimal reconstruction P (114) of the subject image P (102).
  • an optimisation method is employed which is adapted to minimise a measure of reconstruction error, such as the energy or the variance of error signal ⁇ (116) of the model depicted in Figure 1.
  • the measure of reconstruction error accounts for the accuracy of image reconstruction by the inverse model in the absence of additive noise and estimation error, in combination with amplification by the inverse model of additive noises ⁇ and ⁇ . That is, embodiments of the present invention seek to improve over the prior art by optimising not only over the accuracy with which an inverse function of the spatial sensitivity of the receiver coils is established, but also taking into account the extent to which the final reconstructed image may be corrupted due to amplification of additive noise and estimation errors, which is a drawback of existing methods, such as SENSE as described above.
  • the subject image is reconstructed by applying the inverse model to the pMRI signal data S (110). A reconstructed image output may then be provided to an end-user.
  • the step of determining the inverse model may be formulated as an HL norm optimisation problem.
  • the SENSE method may be improved utilising the teaching of the present invention by seeking a solution to the HL norm optimisation problem defined by: min ⁇
  • ⁇ is a weighting factor, which may be predetermined, or determined automatically by adaptive estimation procedures.
  • the optimisation problem defined by equation (18) includes two components, the first of which corresponds with the PR condition addressed by the prior art SENSE method, while the second term corresponds with the gain of the transfer matrix F (112) which may be responsible for undesirable amplification of additive noises.
  • the I-L norm optimisation problem defined by equation (18) can be solved by Linear Matrix Inequality (LMI) optimisation, as now outlined.
  • LMI Linear Matrix Inequality
  • FIG. 2 a schematic diagram illustrating a processing system 200 which is suitable for the implementation of embodiments of the present invention.
  • the system 200 is a computing system having at least one processor 202 interfaced to at least one storage medium 204, typically being a suitable type of memory, such as Random Access Memory, for containing program instructions and transient data related to the operation of the processing system 200, as well as the implementation of operations and methods embodying the invention.
  • the storage medium 204 may also include persistent storage, such as magnetic or optical drive storage, for longer-term storage of programs and data.
  • the processor 202 is also typically interfaced to a peripheral bus 206, or equivalent, which provides access to one or more peripheral interfaces 208.
  • the peripheral interfaces 208 may include one or more input/output devices, including user interface devices such as a keyboard, pointing device, display and so forth, as well as communications interface devices, such as network interface devices, serial/parallel data interface devices, and so forth.
  • peripheral interface devices 208 may be provided enabling the MRI signal data to be entered into the processing system 200, and to enable the output of a reconstructed image, for example on a display device, hard-copy device and/or via a communications data interface.
  • the memory 204 further contains a body of program instructions 210 particularly implementing the various method steps, and computational/numerical procedures required in accordance with an embodiment of the invention, such as those developed in the foregoing description.
  • program instructions 210 particularly implementing the various method steps, and computational/numerical procedures required in accordance with an embodiment of the invention, such as those developed in the foregoing description.
  • various development and execution environments are available that would be suitable for implementation of such methods. These include native code for direct execution by the processor 202, but also encompass dedicated numerical and computational processing environments, such as that provided by the product MATLAB®.
  • Various numerical and signal processing libraries are also available, compatible with a variety of programming languages and environments, which could be used in the implementation of embodiments of the invention. It will accordingly be appreciated that the invention is not limited to any particular means of implementation, in this respect.
  • a processing system generally in accordance with that represented in
  • Figure 2 has been implemented and utilised to illustrate the effectiveness of the present invention, particularly in the embodiment represented by the block diagram 100 of Figure 1 , and equations (18) to (21) above.
  • the H ⁇ optimised reconstruction obtained from this implementation has been compared with the prior art SENSE method, in the simulation described by the following.
  • an array of eight receiver coils has been simulated by numerical calculation (utilising the Biot-Savart law) in order to generate each (simulated) coil sensitivity function.
  • the simulated sensitivity functions are then multiplied with a magnetic resonance image, and Fourier transformed to produce corresponding sampled k-space representations.
  • additive noise ⁇ has been simulated by adding white Gaussian noise samples to the down-sampled k-space data to produce an overall simulated pMRI signal S having a signal-to-noise ratio of 37dB.
  • the above-described H ⁇ optimisation has been performed, to obtain the H ⁇ optimised inverse model F, which is compared with the least squares PR solution of the prior art SENSE algorithm.
  • a relative reconstruction error ⁇ r is defined according to:
  • ⁇ lj,j and lj,j are respectively the absolute reconstruction error and the simulated input at a corresponding pixel of the MRI image.
  • Figure 3A illustrates the results of simulate pMRI image reconstruction 302, in accordance with the prior art SENSE method.
  • Figure 3B illustrates the simulated pMRI image reconstruction 304 in accordance with the aforedescribed embodiment of the present invention.
  • the improvement provided in accordance with this embodiment is clearly visually apparent in the images. This improvement is quantified by the following table of results.
  • the relative reconstruction error in accordance with the embodiment of the present invention is 15.82%, as compared with 81.48% for the prior art SENSE method. It is notable that while the reconstruction in accordance with the present invention does not approximate as closely the perfect reconstruction condition (9.9867x10 " ⁇ as compared to 1.0247x10 '9 in accordance with the prior art method), overall a significant improvement is achieved due to the reduction, by approximately a factor of 100, in the gain (as measured by the Hoo norm) of the inverse function F (3.9529x10 4 in accordance with the present method, as compared with 2.1665x10 6 for the prior art).
  • Figures 4A, 4B and 4C show images derived from a real-world MRI example.
  • Figure 4A shows and MRI image 402 of a slice through the head of a human subject.
  • the image 404 is reconstructed using the prior art (PR) SENSE method, and the quality and clarity of the image 404 are clearly inferior to the unaccelerated image 402.
  • the effects of amplified noise in the reconstructed image 404 are also apparent.
  • the quality and clarity of the image 406 are more closely comparable to the unaccelerated image 402, and are significantly superior to the prior art pMRI reconstruction 404.
  • pMRI imaging in accordance with the present invention provides the potential for clear benefits over the prior art.
  • embodiments of the present invention will enable relevant health professionals to select between a wide variety of tradeoffs between imaging time and image quality via pMRI techniques, while generally having improved outcomes as compared with prior art pMRI methods.
  • Embodiments of the present invention may accordingly find application in a wide variety of situations, including those in which a dynamic picture of internal subject activity is required, including reasonably rapid real-time updates of MRI imagery.
  • Figure 5 shows further images derived from another real-world MRI example, namely a cardiac image generated using an eight channel cardiac coil array.
  • the images 504, 506 have been reconstructed using the prior art SENSE method, whereas the images 508, 510 are H ⁇ optimal reconstructions generated in accordance with the above-described embodiment of the present invention.
  • image reconstruction in pMRI may be considered equivalent to signal reconstruction in a cyclic filter bank (FB) enables additional improvements and benefits to be achieved in the case of auto-calibrating image reconstruction methods, such as GRAPPA.
  • auto-calibrating image reconstruction methods such as GRAPPA.
  • ACS auto-calibrating signals
  • the ACS are acquired by full excitation of a sub-area of k-space, without downsampling, for a calibration period.
  • the number of ACS lines used in the calibration process affects both image quality, and calibration time. The greater the number of ACS lines utilised, the more accurately the coil sensitivity functions may be estimated, but also the greater time that will be required for calibration.
  • the particular lines chosen for calibration may be selected in order to optimise estimation, and in particular it can be shown that the use of central k-space harmonics provides an optimal choice, since these include low-frequency harmonics containing the most energy of the associated image signal.
  • the GRAPPA method may be improved in accordance with preferred embodiments of the invention by reformulating its underlying reconstruction process within the FB framework. More particularly, the synthesis polyphase matrix, or FB, may be decomposed into L subsystems as follows:
  • the synthesis FB subsystems may be estimated using A key insight of the FB interpretation of pMRI reconstruction is that the conventional GRAPPA estimation effectively assumes that the FB is causal, and has finite impulse response (FIR).
  • FIR finite impulse response
  • the synthesis FB may, in general, be noncausal infinite impulse response (MR), even if the analysis FB (Ze polyphase matrix E) has causal FIR characteristics.
  • MR noncausal infinite impulse response
  • image artefacts will inherently be generated in the conventional GRAPPA reconstruction due to the artificial structural constraint that the FB is causal FIR.
  • causal and anti-causal subsystems may be written in left matrix fraction form:
  • Equation (28) may be written in the form of the following linear parameter model
  • Ri, Qi and R 2 , Q 2 are the orders of the causal and anti-causal subsystems respectively, and the A' and B' are the parameter coefficient matrices of subsystem i, as defined by equations (30) and (31).
  • the modelling orders utilised in the experimental embodiment were experimentally determined according to a normalised reconstruction error calculated in a similar manner to equation (22).
  • the resulting orders of the IIR model in all experiments were relatively low, with values of R in the range of 1 to 2, and values of Q in the range of 2 to 5.
  • the experimental embodiment outperforms conventional GRAPPA, and this improvement was also visible in the corresponding reconstructed images (not shown).
  • the experimental embodiment performed better than conventional GRAPPA in all cases, and is able to produce a relatively consistent, and low, level of reconstruction error even when the number of ACS lines is significantly reduced, from 112 to 28.
  • Conventional GRAPPA exhibits higher reconstruction error generally, and significantly increased reconstruction error when the number of ACS lines decreases.
  • the experimental embodiment demonstrates the superiority of noncausal HR FB methods over conventional GRAPPA, resulting from removal of the structural constraints in the prior art methods.

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Abstract

L'invention concerne un procédé, un appareil et un système permettant de reconstituer l'une image d'un sujet dans une machine d'imagerie par résonance magnétique (IRM) comportant une pluralité de bobines réceptrices. En particulier, on effectue une reconstitution d'image par résonance magnétique parallèle (IRMp) par réception de données de signaux d'IRMp comprenant des échantillons numérisés acquis à partir des bobines réceptrices de la machine d'IRM. Un système d'entrée/sortie dynamique d'un processus de détection par IRMp de la machine d'IRM est construit, dans lequel le modèle incarne une pluralité de fonctions de sensibilité spatiale estimées correspondant à chacune de la pluralité de bobines réceptrices. Un modèle inverse est déterminé, qui correspond au modèle du système, au moyen d'un procédé d'optimisation conçu pour minimiser une mesure d'erreur de reconstitution. Plus particulièrement, la mesure d'erreur de reconstitution rend compte de la reconstitution d'image par le modèle inverse en l'absence de bruit de fond supplémentaire et d'une erreur d'estimation, en combinaison avec l'amplification par le modèle inverse du bruit de fond supplémentaire et de l'erreur d'estimation. Une image du sujet est reconstituée par application du modèle inverse aux données de signaux d'IRMp. Une sortie d'image reconstituée peut ensuite être fournie à un utilisateur.
PCT/AU2008/000852 2007-06-14 2008-06-13 Procédé de traitement d'images par résonance magnétique parallèle Ceased WO2008151380A1 (fr)

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AU2007903201A AU2007903201A0 (en) 2007-06-14 Method of parallel magnetic resonance image processing

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CN111989039A (zh) * 2018-04-19 2020-11-24 深透医疗公司 使用深度学习改进磁共振成像的系统和方法
CN113630104A (zh) * 2021-08-18 2021-11-09 杭州电子科技大学 图滤波器的滤波器组频率选择性误差交替优化设计方法
CN113630104B (zh) * 2021-08-18 2022-08-23 杭州电子科技大学 图滤波器的滤波器组频率选择性误差交替优化设计方法

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